Question: $\dfrac{ -3s - 4t }{ -4 } = \dfrac{ -5s + 7u }{ 4 }$ Solve for $s$.
Answer: Notice that the left- and right- denominators are opposite $\dfrac{ -3s - 4t }{ -{4} } = \dfrac{ -5s + 7u }{ {4} }$ So we can multiply both sides by $-4$ $-{4} \cdot \dfrac{ -3s - 4t }{ -{4} } = -{4} \cdot \dfrac{ -5s + 7u }{ {4} }$ $-3s - 4t = - \cdot \left( -5s + 7u \right) $ Distribute the negative sign on the right side. $-3s - 4t = 5s - 7u$ $-{3}s - {4}t = {5}s - {7}u$ Combine $s$ terms on the left. $-{3s} - 4t = {5s} - 7u$ $-{8s} - 4t = -7u$ Move the $t$ term to the right. $-8s - {4t} = -7u$ $-8s = -7u + {4t}$ Isolate $s$ by dividing both sides by its coefficient. $-{8}s = -7u + 4t$ $s = \dfrac{ -7u + 4t }{ -{8} }$ Swap signs so the denominator isn't negative. $s = \dfrac{ {7}u - {4}t }{ {8} }$